This is about a web app that serves images. Since the same request will always return the same image, I want the accessing browsers to cache the images as aggressively as possible. I pretty much want to tell the browser

Here's your image. Go ahead and keep it; it's really not going to change for the next couple of days. No need to come back. Really. I promise.

I do, so far, set

Cache-Control: public, max-age=86400
Last-Modified: (some time ago)
Expires: (two days from now)

and of course return a 304 not modified if the request has the appropriate If-Modified-Since header.

Is there anything else I can do (or anything I should do differently) to get my message across to the browsers?

The app is hosted on the Google App Engine, in case that matters.